A weighted coin has a probability p of showing heads. Is the

[BTGmoderatorDC]

A weighted coin has a probability p of showing heads. Is the value of p > 0.2?


(1) Successive flips are independent, and the probability of getting at least one head in two flips is greater than 0.5.

(2) The probability of getting tail on a flip of coin is less than 0.8.

OA D

Source: Magoosh

[Jay@ManhattanReview]

A weighted coin has a probability p of showing heads. Is the value of p > 0.2?


(1) Successive flips are independent, and the probability of getting at least one head in two flips is greater than 0.5.

(2) The probability of getting tail on a flip of coin is less than 0.8.

OA D

Source: Magoosh

Say the probability of getting a head = p; thus, the probability of getting tail = 1 - p.

We have to determine whether p > 0.2.

Let's take each statement one by one.

(1) Successive flips are independent, and the probability of getting at least one head in two flips is greater than 0.5.

Scenario 1: Head and Tail; Probability = p*(1 - p)
Scenario 2: Both Heads; Probability = p^2

From Statement 1, we have p*(1 - p) + p^2 > 0.5 => p > 0.5. The answer is yes, p > 0.2 Sufficient.

(2) The probability of getting tail on a flip of the coin is less than 0.8.

=> (1 - p) < 0.8 => p > 0.2. Sufficient.

The correct answer: D

Hope this helps!

-Jay
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